President Donald Trump and North Korean leader Kim Jong Un Held a Signing Ceremony

The president said he "developed a very special bond" with the dictator, who he described as "a very talented man" and plans to invite to the White House.

President Donald Trump and North Korean leader Kim Jong Un held a signing ceremony Tuesday that Trump said would "absolutely" lead to the denuclearization of North Korea

"We had a historic meeting and decided to leave the past behind and sign a historic document," Kim said through a translator. "The world will see a major change."

The agreement followed a half-day of meetings centered around U.S. efforts to get North Korea to abandon its nuclear program.

"The letter that we're signing is very comprehensive and I think both sides are going to be very impressed with the result," Trump said.

Trump said they had "developed a very special bond," describing Kim as "a very talented man."

The president characterized their meetings as "very intensive," and said he would invite Kim to the White House.

The summit was historic in and of itself: the first meeting between a sitting American president and his North Korean counterpart.

The first in a series of dramatic moments came as Trump and Kim shook hands Tuesday morning.

As the two men approached each other on a colonnade at the Capella Hotel on Sentosa Island here, with American and North Korean flags interspersed behind them, reporters could hear Kim or his interpreter say, "Nice to meet you, Mr. President."

Then, they posed for photographs, stern-faced, before making their way to a meeting room where they spoke briefly to the media.

"We will have a terrific relationship," Trump said. "I have no doubt."

Kim noted the nascent relationship already has survived serious obstacles — this meeting was planned, canceled and put back on the calendar — in getting to the point where the leaders could talk with each other in person.

"It was not easy to get here," but the two sides "overcame" obstacles, the North Korean leader said through a translator.

"That's true," Trump replied.

That first meeting lasted about 45 minutes. Trump said afterward that their relationship was "very, very good" and "excellent."

That could be meaningful because Trump has placed his emphasis on the personal dynamics of the relationship he forges with Kim, whom American officials say will have to give up his nuclear arsenal and his ability to develop new weapons in order to get relief from crippling U.S. economic sanctions and assurances that the U.S. will not take military action against him.

"It's a great honor to be with you, and I know we'll have tremendous success together," Trump said at the start of a second meeting, which featured the two leaders and their aides. "We'll solve the big problem, the big dilemma, that until this point has been unable to be solved."

Kim did not respond to questions from the media about whether he would give up his nuclear program.

The summit got its official kickoff Tuesday after staff-level talks in recent days "moved more quickly than expected," the White House said.

"The fact that I am having a meeting is a major loss for the U.S., say the haters & losers," Trump also tweeted shortly before the meeting. "We have our hostages, testing, research and all missle (sic) launches have stoped (sic), and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine!"

Before arriving here, Trump said it wouldn't take him long to gauge whether Kim is just looking for a photo-op or is willing to make the kinds of concessions that would end North Korea's decades of isolation.

"I think within the first minute, I'll know — just my touch, my feel," Trump said recently.

The second meeting, which got under way about 10 a.m. local time, was attended by North Korean officials, Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton, in addition to Trump and Kim. The leaders wrapped up their talks with a working lunch.

Pompeo and Bolton have played the good cop/bad cop roles in the administration's negotiations with Pyongyang. Pompeo has previously met with Kim and, as the nation's top diplomat, has a lot invested in striking a deal. Bolton raised eyebrows last month when he began openly discussing using a "Libya model" in negotiations with Kim.

When Bolton worked in President George W. Bush's administration, Libyan leader Moammar Gadhafi gave up his nuclear program under the threat of U.S. military action against him and the promise of sanctions relief. To that point, the parallel could be appealing to Kim.

But Gadhafi ended up dead within a decade following a U.S.-led bombardment of his country. Bolton's use of the Libya phrasing, reiterated by Vice President Mike Pence in an interview, contributed to a tiff between the two nations and the brief cancellation of the summit by Trump. But it was quickly put back on track.

Trump is expected to make one final public appearance in Singapore — a 4 a.m. ET news conference — before leaving Tuesday night to return to Washington.